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  2. Logarithmic derivative - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_derivative

    The logarithmic derivative is then / and one can draw the general conclusion that for f meromorphic, the singularities of the logarithmic derivative of f are all simple poles, with residue n from a zero of order n, residue −n from a pole of order n.

  3. Logarithmic differentiation - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_differentiation

    In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] (⁡) ′ = ′ ′ = (⁡) ′.

  4. Partial derivative - Wikipedia

    en.wikipedia.org/wiki/Partial_derivative

    If the direction of derivative is not repeated, it is called a mixed partial derivative. If all mixed second order partial derivatives are continuous at a point (or on a set), f is termed a C 2 function at that point (or on that set); in this case, the partial derivatives can be exchanged by Clairaut's theorem:

  5. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): (⁡) ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.

  6. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    The basic way to maximize a differentiable function is to find the stationary points (the points where the derivative is zero); since the derivative of a sum is just the sum of the derivatives, but the derivative of a product requires the product rule, it is easier to compute the stationary points of the log-likelihood of independent events ...

  7. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    Partial derivatives are generally distinguished from ordinary derivatives by replacing the differential operator d with a "∂" symbol. For example, we can indicate the partial derivative of f(x, y, z) with respect to x, but not to y or z in several ways: = =.

  8. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  9. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...